Commutator of maximal operator on Carleson curves in local generalized weighted Morrey spaces

Abstract

We study the maximal commutators Mb,? and the commutators of the maximal operator [b,M?] over the local generalized weighted Morrey spaces LM{t0} p,? (?, w) and the generalized weighted Morrey space Mp,? (?,w) defined on Carleson curves ?. We give necessary conditions of the boundedness of the maximal commutators Mb,? and the commutators of the maximal operator [b,M?] in the local generalized weighted Morrey space LM{t0} p,? (?,w) and the generalized weighted Morrey space Mp,? (?,w) defined on Carleson curves ?, respectively. © 2010 jcam All rights reserved.